For starters, don't hang on to the gutter! You may pull it down.
I'm not surprised to hear about the problem you're having in getting someone to fix your gutter. Here, at my work, we have potential hires and interviewees either not showing up for the interview, not showing up after we hire them ('cause they decided to stay where they are now), not showing up for their interviews ('cause they forgot), coming in after we hire them only to tell us they took a job elsewhere, asking for an office with a window, and on and on and on. So don't feel too bad about what's happening to you. It's happening EVERYWHERE.
In any event, you may be able to find just a general carpenter to fix your problem. Just ask if he/she has experience hanging/re-hanging gutters. Of course, have him clean the gutter out. I'd suspect that the 'droop' is where 2 pieces of gutters meet. If this is the case, do mention this to the guy (if you're talking to him on the phone), because you'll want him to caulk up the joint when he's done so it doesn't leak. If not, you or your husband can do it. (Just buy some Gutter Caulk at the Home Center, clean and dry the joint, and apply the caulk. It's important that is clean AND dry!)
As an aside, if you eventually get new gutters, find a gutter contractor that makes SEAMLESS Gutters. (Obviously, they are gutters w/o seams.) They're actually bent and folded on-site to the exact length that's needed! Isn't that neat???! They even make a 'hidden gutter hanger' for gutters so you don't see those 'gutter nails' falling out all the time! (This is probably what happened to your gutter.)
You have to realize that leaning a ladder up agains a gutter can be dangerous, especially in YOUR case where the gutter is, most likely, loose! At the same time, if the gutter needs re-hanging, the work will have to either be done from above (up on the roof), or from just below (with the ladder up against the house). Either way, it can be intimidating and unsafe if you're not use to, or comfortable with, working from such contorted positions. One can very easily lose their balance or sense of orientation, and fall. So do be careful!